Polarization mode dispersion (hereinafter, “PMD”) is an optical property that can be generated by a concatenation of two or more birefringent elements. PMD can be a significant impairment in high data-rate optical communication systems when the transmission medium is optical fiber. Data transmission rates that are effected by the PMD of optical fiber are typically 10 Gbps, 40 Gbps, and higher.
Optical fiber can exhibit PMD because of imperfections within the fiber, which induce localized birefringence. When the transmission path is long, these localized birefringent sections can combine to yield a particularly complicated polarization-dependent effect. These localized sections are known to result, for example, from eccentricities of the waveguide's core, micro-bubbles in the waveguide core and/or cladding, and strain gradients through the fiber cross-section. Mechanical stress on the fiber resulting from cabling and installation can also cause the fiber to suffer stress-induced birefringence. Environmental changes experienced by a fiber can be dynamic and statistical in nature, and are believed to result in PMD changes that can last for variable periods of time and vary with wavelength, with the potential for prolonged degradation of data transmission.
In the laboratory and the field, there are reasons to artificially generate PMD in a controlled fashion.
In the laboratory, for example, a PMD emulator is desirably used to predictably and repeatably add PMD to signals generated by optical transmitters for testing optical receivers. In many cases, however, the center frequency of the optical signal being tested may not be properly aligned with the PMD spectrum generated by the emulator. Because a conventional PMD emulator cannot controllably “frequency shift” its spectrum to accommodate for the misalignment, those attempting to evaluate the PMD response of receivers and other equipment are generally forced to test undesirable and unpredictable PMD states. Often, PMD emulators include ten or more birefringent sections.
A PMD generator can also be incorporated into a specialized telecommunications sub-system called a PMD compensator. PMD compensators are used to mitigate the deleterious effects of PMD imparted on an optical data signal transmitted through an optical fiber. In contrast to PMD emulators, PMD compensators generally include only one or two birefringent sections, but such a small number of sections greatly limits the range of achievable PMD states. In order to achieve a greater operating range, it may be desirable to use PMD compensators that include more than two birefringent generator sections. Unfortunately, PMD spectra generated with more than two sections are difficult to control, subject to misalignment, and are frequency dependent.
The number of birefringent sections is known to at least partially determine how much structure exists in the resultant PMD magnitude spectrum. If one were to take the Fourier transform of an exemplar PMD-magnitude spectrum artificially generated by several birefringent sections, several Fourier component frequencies would be evident. The number of sinusoidal Fourier components depends generally on the number of birefringent sections. For example, one birefringent section generates a PMD-magnitude spectrum that has only one Fourier component, the average, or DC, component. Two birefringent sections also generate a PMD spectrum whose magnitude also has only one Fourier component, again the DC component. Each additional birefringent section can generate multiple sinusoidal Fourier components that appear in the resultant PMD spectrum.
It is known that a concatenation of several birefringent sections can be used to synthesize a particular optical intensity spectrum. For example, in 1949 Evans, an astronomer, described a birefringent filter to improve solar observations (see, Evans “The Birefringent Filter,” J. Optical Soc. of America, Vol. 39, No. 3, at 229-242 (March, 1939)) (hereinafter, “Evans”). Similarly, in 1961 Harris described a generalized filter synthesis method using birefringent filters (see, Harris et al. “Optical Network Synthesis Using Birefringent Crystals,” J. Optical Soc. of America, Vol. 54, No. 10, at 1267-1279 (March, 1964)) (hereinafter, “Harris”). In both cases, a multi-stage birefringent filter was placed between two polarizers to generate an optical intensity spectrum.
Bührer U.S. Pat. No. 4,987,567 (hereinafter, “Bührer”) describes an alternative device that includes a multi-stage birefringent filter between two polarization diversity stages. According to this design, optical power transmission was increased, albeit in the form of two optical beams. Buhrer's design has been extended to optical interleavers (see, e.g., U.S. Pat. Nos. 6,301,046, 6,215,923, 6,212,313, and 6,252,711).
Thus, Evans, Harris, and Bührer showed coherent birefringent filters. As used herein, a coherent birefringent filter is one in which each of the birefringent elements exhibits an optical retardation that is an integral multiple of a unit reference optical retardation, which must itself be an integral multiple of 2π.
Fourier analysis of the resultant optical intensity spectrum generated by such coherent birefringent filters can, in general, reveal multiple sinusoidal frequency components. Moreover, it is known that the relative phase between each periodic component can be fixed to zero. A filter that exhibits multiple Fourier components having identical phase values, as transformed from an optical intensity spectrum, is referred to herein as a coherent filter. In general, a coherent optical filter exhibits high periodicity and high contrast ratio in its optical intensity spectrum.
Unlike the optical filtering shown by Evans, Harris, and Bührer, PMD generation does not permit frequency-dependent loss nor does it permit polarization-dependent loss. Unfortunately, the polarizers used by Evans and Harris generally produce substantial frequency-dependent and polarization-dependent losses. Also, the polarization diversity scheme shown by Bührer causes frequency-dependent loss on at least one of the output beams.
As mentioned above, it is known that PMD generators can be constructed from concatenated polarization maintaining (hereinafter, “PM”) fibers. Rotation of fibers with respect to adjacent fibers can be coordinated in such a manner to generate various forms of PMD spectra. For example, I. T. Lima et al. reports a PMD emulator constructed with 15 polarization maintaining fibers and intermediate rotatable connectors (see, Lima et al., “Polarization Mode Dispersion Emulator,” OFC 2000, Paper ThB4 (February 2000)). Alternatively, a PMD generator can be constructed with a concatenation of birefringent crystals. In this case, rotation of adjacent birefringent crystals (or control of intermediate polarization-transforming stages) can also be coordinated in such a manner to generate various forms of PMD spectra. For example, a PMD emulator can be constructed with 12 birefringent crystals (see, Damask, “A Programmable Polarization-Mode Dispersion Emulator for Systematic Testing of 10 Gb/s PMD Compensators,” OFC 2000, Paper ThB3 (March, 2000)). None of the references, however, shows how to build a coherent PMD generator.
It would therefore be desirable to provide methods and apparatus for controllably generating coherent PMD spectra.
It would also be desirable to provide methods and apparatus to for generating coherent PMD spectra that coincide with the comb spectrum of a WDM optical communications system.
It would be further desirable to provide methods and apparatus to control coherent artificial PMD generation to independently generate first and second order PMD.